Mayan priests started off ceremonies aimed at marking the end of the current era in the Mayan long-count calendar Thursday, with dancing, incense and rituals designed to thank the gods.

The Mayas performed the "New Fire" ceremony at a park in Mexico City, but complained they have been barred by authorities from performing rituals at their ancestral temples in the Maya region.

The Mayas measure time in 394-year periods known as Baktuns. The 13th Baktun ends around Dec. 21, and 13 is considered a sacred number for the Maya.

The estimated 800,000 surviving Mayas in Mexico are hoping for a better new Baktun than the one now ending, which began around 1618. It included the painful aftermath of the Spanish conquest in which Mayas and other indigenous groups saw their temples and sacred writings systematically destroyed and their population decimated by European diseases and forced labor.

"This is the ending of an era for the Maya, an era which has been very intense for us, in which we have had suffering and pain," said Mayan priest Jose Manrique Esquivel, 52, who wore a feather headdress and body paint for the ceremony. For the new Baktun, he said, "we are praying the wars, the conflicts, the hunger to end."

The priest, who is in agreement with most archaeologists and astronomers, doesn't believe the ancient Mayas predicted the world would end with the close of the current Baktun. Some bloggers and astronomy enthusiasts have suggested the Mayan calendar would "run out" on Dec. 21.